MinT - Best Known (157−42, 157, s)-Nets in Base 8

Best Known (157−42, 157, s)-Nets in Base 8

(157−42, 157, 1026)-Net over F₈ — Constructive and digital

Digital (115, 157, 1026)-net over F₈, using

t-expansion [i] based on digital (114, 157, 1026)-net over F₈, using
- 15 times m-reduction [i] based on digital (114, 172, 1026)-net over F₈, using
  - trace code for nets [i] based on digital (28, 86, 513)-net over F₆₄, using
    - net from sequence [i] based on digital (28, 512)-sequence over F₆₄, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 28 and N(F) ≥ 513, using
        the Hermitian function field over F₆₄ [i]

(157−42, 157, 6642)-Net over F₈ — Digital

Digital (115, 157, 6642)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(157−42, 157, 6999491)-Net in Base 8 — Upper bound on s

There is no (115, 157, 6999492)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 6097 177226 998268 624744 082343 703317 338065 854290 813340 834925 391606 147674 227790 828197 722564 342640 391100 225996 914537 197184 915702 007512 460487 553200 > 8¹⁵⁷ [i]